System, method and computer-accessible medium for highly-accelerated dynamic magnetic resonance imaging using golden-angle radial sampling and compressed sensing

ABSTRACT

Exemplary method, system and computer-accessible medium can be provided which facilitates an acquisition of radial data, which can be continuous, with an exemplary golden-angle procedure and reconstruction with arbitrary temporal resolution at arbitrary time points. According to such exemplary embodiment, such procedure can be performed with a combination of compressed sensing and parallel imaging to offer a significant improvement, for example in the reconstruction of highly undersampled data. It is also possible to provide an exemplary procedure for highly-accelerated dynamic magnetic resonance imaging using Golden-Angle radial sampling and multicoil compressed sensing reconstruction, called Golden-angle Radial Sparse Parallel MRI (GRASP).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application relates to and claims priority from U.S. PatentApplication No. 61/635,792, filed on Apr. 19, 2012, the entiredisclosure of which is incorporated herein by reference.

FIELD OF THE DISCLOSURE

The present disclosure generally relates to medical imaging apparatusand/or methods, and in particular to exemplary embodiments forhighly-accelerated dynamic magnetic resonance imaging (“MRI”) usinggolden-angle (“GA”) radial sampling and multicoil compressed sensingreconstruction or Golden-angle Radial Sparse Parallel (“GRASP”) MRI.

BACKGROUND INFORMATION

Traditional MRI can provide several advantages compared to other imagingmodalities (e.g., computed tomography (“CT”)), such as a superiorsoft-tissue characterization, absence of an ionizing radiation andflexible image contrast, etc. However, conventional MRI techniques canbe relatively slow, which can limit temporal and spatial resolution andvolumetric coverage, and can introduce motion related artifacts. In MRI,the imaging data can be commonly acquired as samples of the Fouriertransform of the object to be reconstructed (e.g., a spatial distributedset of NMR signal sources that can evolve in time). The imagereconstruction process can involve recovering an estimate (e.g., animage) of the original object from these samples. As only a limitednumber of these samples of the Fourier transform (e.g., “k-space”) canbe acquired at a time, with a delay between each such data set acquiredimposed by the signal excitation and encoding process, the total timefor data acquisition can be dependent on the spatial and temporal imageresolution desired, and the size of the object. 3D image data cansimilarly be more time-consuming than 2D imaging. In order to reduce theimage acquisition time (e.g., in order to more accurately capture movingobjects, such as the heart, or to minimize the risk of patient motionduring the data acquisition, which can lead to artifacts, or simply toreduce the total time for the MRI examination), more efficient ways ofaccurately reconstructing the image from a reduced number of k-spacesamples can be needed.

Some recent methods for reducing the amount of k-space sampling forimage reconstruction can include: a) radial sampling of k-space withoutloss of generality, (the orientations of these radial samples can bedesignated as lying in the k_(x)-k_(y) plane, which can be more robustto undersampling by presenting low-value streaking aliasing artifacts inthe reconstructed image, distributed over the complete field of view);b) spiral sampling of k-space, which can acquire more samples peracquisition which can have similar benefits to radial sampling inreconstruction of radial sampling, and which can be considered as aspecial case of spiral sampling); c) golden-angle ordering of theacquisition of the radial sets of samples, which can help to maintain afairly uniform distribution of sampling locations while differentamounts of radial k-space data can be acquired; and d) using compressedsensing or sampling (“CS”) approaches to image reconstruction, which canrely on the compressibility of the final images to reduce the amount ofimaging k-space data to be acquired, at the cost of increasedcomputational effort in the image reconstruction process.

There has been prior work on producing faster 3D MRI by combining 2Dradial sampling with the use of golden-angle ordering for the sequenceof the radial sample acquisitions, with a regularly spaced set ofsamples acquired in the remaining (e.g., “k_(z)”) direction, thusproducing a “stack of stars” sampling pattern in k-space (FIG. 1E). Thisapproach to 3D MRI can be further accelerated by combining it with CSimage reconstruction methods, thus enabling equivalent quality imagereconstruction from a sparser, and more rapidly acquired, set of k-spacesamples (See e.g., References 16 and 19). This can also provideincreased flexibility in trading off relative optimization of theimaging time and the effective temporal resolution and sampling densityof the final images during the image reconstruction, which can bevaluable for dynamic imaging.

CS procedures (See, e.g., References 1-3) can provide a rapid imagingapproach, exploiting image sparsity and compressibility. Instead ofacquiring a fully-sampled image and compressing it afterwards (e.g.,standard compression), CS takes advantage of the fact than an image canusually be sparse in some appropriate basis, and can reconstruct thissparse representation from undersampled data, for example, without lossof important information. Successful applications of CS generally useimage sparsity and incoherent measurements. MRI can provide these twobasic preferences, since (a) medical images can naturally becompressible by using appropriate sparsifying transforms, such aswavelets, finite differences, principal component analysis (“PCA”) andother techniques, and (b) MRI data can be acquired in the spatialfrequency domain (e.g., k-space) rather than in the image domain, whichcan facilitate the generation of incoherent aliasing artifacts.Moreover, CS can be combined with previous acceleration methods in MRI,such as parallel imaging, to further increase the imaging speed.

Parallel imaging can be a traditional acceleration technique in MRI thatcan employ multiple receiver coils with different spatial sensitivitiesto reconstruct images from regularly undersampled k-space data.Combinations of CS and parallel imaging have been provided in severalvariants, for example using the notion of joint multicoil sparsity,where sparsity can be enforced on the signal ensemble from multiplereceiver coils rather than on each coil separately (See, e.g.,References 4-8).

Dynamic MRI can be used for CS, due to (a) extensive correlationsbetween image frames which can typically result in sparserepresentations after applying an appropriate temporal transform, suchas FFT, PCA or finite differences, which can be equivalent to totalvariation (“TV”) minimization, and (b) the possibility of using adifferent random undersampling pattern for each temporal frame, whichcan increase incoherence, and can distribute the incoherent aliasingartifacts along the temporal dimension which can result in artifactswith lower intensity (See, e.g., References 8-10).

Significant amount of current work on CS MRI uses random undersamplingof Cartesian k-space trajectories to increase data acquisition speed.However, in Cartesian trajectories, it can be possible that onlyundersampling of phase-encoding dimensions (e.g., y and z) can accountfor faster imaging, which can limit the performance of compressedsensing, since incoherence and sparsity along the other spatialdimension (e.g., x) cannot be exploited. Radial k-space sampling canprovide an attractive alternative for compressed sensing MRI, due to theinherent presence of incoherent aliasing artifacts along all spatialdimensions, even for regular undersampling. Although the readoutdimension can also be fully-sampled in radial MRI, the situation can bedifferent from Cartesian MRI, since skipping radial lines caneffectively undersample all spatial dimensions, which can distribute theoverall acceleration along these dimensions and can result in loweraliasing artifacts.

Radial trajectories can be less sensitive to motion, which canfacilitate a better performance in capturing dynamic information. FIGS.1A-1D show illustrations associated with a highly increased incoherenceof radial sampling compared to Cartesian sampling for static and dynamicimaging, which can be due to the inherent presence of low-valuestreaking aliasing artifacts that can spread out along all spatialdimensions in radial sampling. For example, FIGS. 1A-1D illustrate ak-space sampling patterns, point spread functions (“PSFs”) andincoherence of Cartesian and radial trajectories with 12.8-foldacceleration for static and dynamic imaging. The PSFs can be computed byapplying an inverse Fourier transform to the k-space sampling mask,where the sampled positions can be equal to 1, and the non-sampledpositions can be equal to 0. The standard deviation of the PSF sidelobes can be used to quantify the power of the resulting incoherentartifacts (e.g., pseudo-noise). Incoherences can be computed using themain-lobe to pseudo-noise ratio of the PSF (See, e.g., References 3).The PSFs for dynamic imaging can be computed in the space of temporalfrequencies, after a temporal FFT, which can be usually employed tosparsify dynamic MRI data. Compressed sensing radial MRI using regularundersampling of radial trajectories has been previously described andsuccessfully applied to cardiac perfusion (See, e.g., Reference 11),cardiac cine (See, e.g., Reference 12), and breast MRI (See, e.g.,Reference 13). However, even though these studies can use coil arrays,only coil-by-coil reconstructions can be performed, which can limit theperformance. Furthermore, the acquisition trajectory can be limited toskipping a specific number of radial lines, which can present only alimited gain in incoherence. Other radial MRI techniques can lead tobetter performance in CS. For example, the golden-angle acquisitionprocedure (See, e.g., Reference 14) can be utilized, where radial linescan be continuously acquired with an angular increment of 111.25°, suchthat each line can provide complementary information. Uniform coverageof k-space can be accomplished by grouping a specific number ofconsecutive radial lines, which can lead to improved temporalincoherence. Moreover, golden-angle radial acquisition can enablecontinuous data acquisition and reconstruction with arbitrary temporalresolution by grouping a different number of consecutive radial lines toform each temporal frame.

In dynamic imaging procedures, where a time-series of images can beacquired to visualize organ function or to follow the passage of acontrast agent, spatial resolution and volumetric coverage can usuallybe sacrificed in order to maintain an adequate temporal resolution andreduce motion-related artifacts.

Respiratory motion can degrade image quality, and reduce the performanceof compressed sensing (See e.g., Reference 15) since temporal sparsitycan be decreased. To minimize the effects of respiratory motion, MRIdata acquisition can be performed during breath-holds, or usingnavigator or respiratory-bellow gating. However, breath-holds can besubject dependent, with limited duration in patients, and the use ofnavigator or respiratory-bellow gating can utilize long acquisitiontimes to acquire data during an interval of moderate respiratory motion.Non-Cartesian imaging procedures can offer self-gating by estimating therespiratory-motion signal from the oversampled k-space center. However,current gating techniques can be inefficient since they only use thedata acquired during an interval of moderate respiratory motion (e.g.,expiration) and discard the rest, which can correspond to a largepercentage of the total amount of acquired data.

Thus, it may be beneficial to provide an exemplary imaging apparatusthat can combine carious CS, golden-angle, and parallel imagingprocedures to decrease the image acquisition time, while maintaining ahigh level of image quality, and which can overcome at least some of thedeficiencies described herein above.

SUMMARY OF EXEMPLARY EMBODIMENTS

To address at least some of these drawbacks and/or deficiencies,arrangement, system, method and computer-accessible medium according tocertain exemplary embodiments of the present disclosure can utilizecontinuous acquisition of radial data with golden-angle scheme andreconstruction with arbitrary temporal resolution at arbitrary timepoints, along with a combination of compressed sensing and parallelimaging to offer a significant improvement, for example in thereconstruction of highly undersampled data.

Systems, methods and computer-accessible mediums for reconstructing dataassociated with an object(s) can be provided which can include, forexample, continuously acquiring radial data based on a golden-angleprocedure, sorting the acquired radial data into a time-series witharbitrary temporal resolution, and reconstructing the data using acompressed sensing procedure and a parallel imaging procedure. Theradial data can include magnetic resonance imaging data, and the radialdata can comprise a plurality of radial lines. In certain exemplaryembodiments of the present disclosure, the radial lines can have agolden-angle separation of approximately 111.25°.

In some exemplary embodiments of the present disclosure, the arbitrarytemporal resolution can be based on a particular number of consecutiveones of the radial lines, which can be less than a number associatedwith a Nyquist rate. The reconstruction procedure can be performed basedon a first group of consecutive ones of the radial lines used togenerate at least one temporal frame, and based on a second group of theconsecutive ones of the radial lines used to generate a further temporalframe(s), the second group having different radial lines than the firstgroup. In certain exemplary embodiments of the present disclosure, thereconstruction procedure can be performed based on a target shape foreach temporal frame, which can be a boxcar.

In some exemplary embodiments of the present disclosure, thereconstruction procedure can be performed at arbitrary time points bycentering a group of consecutive ones of the radial lines at differentpoints during an acquisition period. The acquiring procedure cancomprise acquiring all slices for a given projection for a particulargolden-angle before proceeding to a next golden-angle.

In certain exemplary embodiments of the present disclosure, theobject(s) can include an anatomical structure(s), and the reconstructionprocedure can be performed based on a physiological motion of theanatomical structure(s). The physiological motion can be an expiratoryphase of the anatomical structure(s), and the expiratory phase can bebased on a respiratory motion signal of the anatomical structure(s). Insome exemplary embodiments of the present disclosure, a cleansing of thephysiological motion using a band pass filter can be performed.

In certain exemplary embodiments of the present disclosure, thereconstruction procedure can be performed based on coil sensitivity mapsof an exemplary multicoil reference image(s), which can be based on aNon-Uniform Fast Fourier Transform. In some exemplary embodiments of thepresent disclosure, the reconstruction procedure can be performed basedon re-sorting the radial data into highly undersampled temporal framesby grouping a particular number of consecutive ones of the radial linesto form each temporal frame, where the particular number can be aFibonacci number.

In certain exemplary embodiments of the present disclosure, the radialdata can be based on k-space sampling of the at least one object. Thek-space sampling can be performed using a stack-of-stars procedure, orusing a stack-of-spiral procedure.

These and other objects, features and advantages of the presentdisclosure will become apparent upon reading the following detaileddescription of exemplary embodiments of the present disclosure, whentaken in conjunction with the accompanying exemplary drawings andappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages of the present disclosure willbecome apparent from the following detailed description taken inconjunction with the accompanying Figures showing illustrativeembodiments of the present disclosure, in which:

FIGS. 1A-1D are sets of illustrative images of various data elements;

FIG. 1E is an exemplary stack-of-stars k-space sampling pattern withradial samples;

FIG. 2 is an illustration of a data acquisition scheme according toexemplary an embodiment of the present disclosure;

FIG. 3 is a set of exemplary illustrations of sampling patterns andexemplary images of conventional non-uniform fast Fourier transformreconstructions;

FIG. 4A is an illustration of an exemplary GRASP acquisition procedurein the 2D space according to an exemplary embodiment of the presentdisclosure;

FIG. 4B is an illustration of an exemplary GRASP acquisition procedurein the 3D space according to an exemplary embodiment of the presentdisclosure;

FIGS. 4C and 4D are illustrations of exemplary filters obtained usingexemplary GRASP for a respiratory signal and a cardiac signal accordingto an exemplary embodiment of the present disclosure;

FIG. 5 is a diagram of a GRASP reconstruction pipeline procedureaccording to an exemplary embodiment of the present disclosure;

FIG. 6 is an exemplary illustration of an exemplary rod-of-rays k-spacesampling pattern with radial samples at more continuous locations withina cylindrical volume according to an exemplary embodiment of the presentdisclosure;

FIG. 7 is an exemplary illustration of an exemplary golden-angle sampleprocedure to select sequential sampling location according to anexemplary embodiment of the present disclosure;

FIG. 8A is a set of exemplary illustration of non-linear remapping andwrapping along a circumference of a circle according to an exemplaryembodiment of the present disclosure;

FIG. 8B is an exemplary illustration of an exemplary golden-anglesampling with approximately uniform sampling density distributionaccording to an exemplary embodiment of the present disclosure;

FIG. 8C is an exemplary illustration of an exemplary golden-anglesampling showing reciprocal non-uniform distribution of sample locationaccording to an exemplary embodiment of the present disclosure;

FIG. 8D is an exemplary illustration of an azimuthal angle and altitudeexemplary for an exemplary golden-angle sampling procedure according toan exemplary embodiment of the present disclosure;

FIG. 9 is a set of exemplary images and graphs related to areconstruction of acquire free-breathing contrast-enhanced volumetricliver MRI data according to an exemplary embodiment of the presentdisclosure;

FIG. 10 is a set of exemplary images related to a reconstruction ofreal-time cardiac cine MRI data acquired according to an exemplaryembodiment of the present disclosure;

FIG. 11A is a set of exemplary images of end diastolic (top image) andend systolic (bottom image) reconstructed with data self-gated inexpiration according to an exemplary embodiment of the presentdisclosure;

FIG. 11B is a set of exemplary images of end diastolic (top image) andan end systolic (bottom image) reconstructed from multiple respiratoryphases an exemplary embodiment of the present disclosure;

FIG. 12A is an exemplary image of a free breathing liver from anexemplary partition without self-gating according to an exemplaryembodiment of the present disclosure;

FIG. 12B is an exemplary image of a self-gated liver with onerespiratory phase according to an exemplary embodiment of the presentdisclosure;

FIG. 12C is an exemplary image of a self-gated liver with multiplerespiratory phases constituting an additional dynamic dimensionaccording to an exemplary embodiment of the present disclosure; and

FIG. 13 is an exemplary system, including an exemplarycomputer-accessible medium, according to an exemplary embodiment of thepresent disclosure.

Throughout the drawings, the same reference numerals and characters,unless otherwise stated, are used to denote like features, elements,components, or portions of the illustrated embodiments. Moreover, whilethe present disclosure will now be described in detail with reference tothe figures, it is done so in connection with the illustrativeembodiments and is not limited by the particular embodiments illustratedin the figures and accompanying claims.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

According to certain exemplary embodiments of the present disclosure,devices, methods, and computer readable mediums can be provided for ahighly-accelerated free-breathing volumetric dynamic MRI technique namedGRASP MRI, for example, using continuous acquisition of radial MRI datawith a golden-angle procedure and multicoil compressed sensingreconstruction. According to certain exemplary embodiments, it can bepossible to provide and/or utilize a synergetic combination of exemplarycompressed sensing, exemplary parallel imaging and exemplarygolden-angle radial trajectories, which can deliver improvedcombinations of temporal resolution, spatial resolution and volumetriccoverage for dynamic MRI studies without breath-holding.

Exemplary Data Acquisition

FIGS. 1A-1D illustrate exemplary k-space sampling patterns, PSFs andincoherences of Cartesian and radial trajectories with 12.8-foldacceleration for static and dynamic imaging. The PSFs can be determinedby applying an inverse Fourier transform to the k-space sampling mask,where the sampled positions can be equal to 1, and the non-sampledpositions can be equal to 0. The standard deviations of the PSFs sidelobes can be used to quantify the power of the resulting incoherentartifacts (e.g., pseudo-noise). Incoherence can be computed using themain-lobe to pseudo-noise ratio of the PSF. The PSFs for dynamic imagingcan be determined in the space of temporal frequencies, after a temporalFast Fourier Transform (“FFT”), which can usually be employed tosparsify dynamic MRI data. Radial sampling can offer a highly increasedincoherence compared to Cartesian sampling for static and dynamicimaging, which can be due to the inherent presence of low-valuestreaking aliasing artifacts that can spread out along all spatialdimensions in radial sampling.

FIG. 2 shows an exemplary data acquisition procedure 210 for the GRASPwith continuous acquisition of radial lines with golden-angle separation(e.g., 111.25°) without pre-defining temporal frames, in accordance withan exemplary embodiment of the present disclosure. FIG. 2 alsoillustrates an exemplary sorting procedure 220 of the exemplary acquireddata to form the time-series of images using a specific number ofconsecutive radial lines for each temporal frame, in accordance with anexemplary embodiment of the present disclosure. The number of radiallines for each temporal frame can be much lower than the, for example,the Nyquist rate. Different temporal resolutions can be obtained byusing a different number of radial lines for each temporal frame.

The exemplary golden-angle separation can provide a different k-spacetrajectory for each radial line, which can produce strongly uncorrelatedor incoherent measurements for improved compressed sensingreconstructions. The same data set can also be used to reconstructdynamic exemplary magnetic resonance (“MR”) images with differenttemporal resolutions, by grouping a different number of consecutiveradial lines to create each temporal frame. The reconstruction can alsobe performed at arbitrary time points, by centering the group ofconsecutive radial lines at different points during the acquisitionperiod.

The exemplary golden-angle procedure can be similar to the acquisitionof k-space lines with random ordering, which can decrease thecorrelation between consecutive spokes, and can provide more incoherentmeasurements. This can be important for contrast-enhanced studies, wherethe signal intensity can change over time. To illustrate the exemplaryadvantage for contrast-enhanced studies, linear and golden-angle radialacquisition of liver perfusion data can be compared, as illustrated inFIG. 3, which shows a set of exemplary illustrations of samplingpatterns and exemplary images of conventional non-uniform FFT (“NUFFT”)reconstructions. Even though the PSF for both methods can be similar,which can be expected due to the fact that the PSF only takes intoaccount the final sampling pattern, and not the signal evolution overtime, exemplary images that can be acquired with the exemplarygolden-angle procedure present lower incoherent artifacts, which can bedue to the more uniform coverage of k-space per unit time provided bygolden-angle acquisitions over standard linear radial sampling. Uniformcoverage of k-space can be facilitated by the exemplary golden-angleprocedure after the acquisition of a few spokes, unlike in standardlinear radial sampling, which can facilitate the acquisition of asubstantially larger number of spokes to cover k-space.

FIG. 3 further shows an exemplary sampling pattern and correspondingpoint spread function PSF for radial MRI with conventional linearprogressive coverage of k-space (e.g., linear sampling) andgolden-angle, for example section 310. The exemplary progression fromblack to gray can denote the exemplary order in which the spokes can beacquired (e.g., black spokes can be acquired first). The exemplaryimages of section 320 show a conventional NUFFT reconstruction of radialliver MRI data acquired with linear sampling and golden-angle. TheNyquist rate can use 400 spokes.

Exemplary volumetric acquisitions can be performed using, for example(a) stack-of-stars (e.g., Cartesian sampling along k_(z) and radialsampling along k_(y)-k_(x)) and (b) 3D golden-angle radial trajectories.Stack-of-stars trajectories can be simpler to implement and canfacilitate parallel reconstruction of different slices after applying aFFT along k_(z). However, such trajectories can fail to take advantageof the incoherence along k_(z). Exemplary 3D golden-angle radialtrajectories can acquire complementary spokes in 3D k-space by using 2Dgolden ratios, for example α=0.4656 and β=0.6823 to calculate theincrements Δk_(z)=2α and Δφ=2πβ for between consecutive spokes, where Δφcan be the angular increment in the k_(y)-k_(z) plane. Exemplary 3Dgolden-angle trajectories can have the same or similar properties of 2Dgolden-angle trajectories, although with an increased incoherence forvolumetric acquisitions.

Exemplary Data Acquisition, Self-Gating and Retrospective Data Sorting

FIG. 4 shows an illustration of an exemplary acquisition for GA radialsampling employed in GRASP (See, e.g., Reference 15). To performself-gating in 3D imaging, most or all slices for a given projectionangle can be acquired sequentially before proceeding to the next angle.The k-space center (k_(x)=k_(y)=0 for 2D and k_(x)=k_(y)=k_(z)=0 for 3D)in each projection angle (e.g., 405 in FIGS. 4A and 4B) can be used toobtain the temporal variation caused by physiological motion such asrespiratory or cardiac motion. Clean motion signals can be obtained witha band-pass filter (FIGS. 4C and 4D). In cardiac imaging procedures,where signal variation can include both respiratory and cardiac motionoccurring simultaneously and with different temporal frequencies, themotion signals can be separated by performing a band-pass filtercentered at each frequency (See, e.g., Reference 17). For multicoilacquisitions, coil elements that can be close to the heart, and aliver-lung interface can be used for respiratory and cardiac gatingrespectively, as shown in 4C and D. Given the detected respiratorymotion signal, the data corresponding to the expiratory phase can firstbe gated for reconstruction (SG-GRASP data). In another exemplaryapproach, most or all the acquired data can be sorted into differentrespiratory phases, to form the additional respiratory-phase dimension(SG-MP-GRASP data). Both sorted data sets can be undersampled. Element410 provided in FIG. 4D cancan indicate gated respiratory phases withequal numbers of spokes in each phase.

Exemplary Image Reconstruction

FIG. 5 shows a diagram of an exemplary GRASP reconstruction pipeline,according to an exemplary embodiment of the present disclosure. First,coil sensitivity maps 510 can be determined/computed using an exemplarymulticoil reference image 515 given by the coil-by-coil inverse NUFFTreconstruction 520 of a composite k-space data set that results fromgrouping together all acquired spokes. This exemplary fully-sampledmulticoil reference image can effectively represent the temporal averageof all acquired spokes, which although can contain temporal blurringartifacts, can provide sufficient information to extract the exemplarysmooth coil sensitivity maps 510 which may not change over time. Second,the continuously acquired golden-angle radial data 525 can be resortedat 530 into highly-undersampled temporal frames 535 by grouping specificnumber (e.g., a Fibonacci number) of consecutive spokes to form eachtemporal frame 535 according to the desired temporal resolution. TheGRASP reconstruction procedure 540 can then be applied to the resortedmulticoil radial data to produce the unaliased image time-series (e.g.,x-y-t) 550.

The exemplary GRASP reconstruction procedure can utilize a combinationof compressed sensing and radial parallel imaging which can enforcejoint sparsity in the multicoil signal ensemble subject to parallelimaging data consistency. The exemplary radial parallel imaging modelcan use a NUFFT operator according to the radial sampling trajectory foreach temporal frame and the computed coil sensitivities to form theencoding equation. The mathematical formulation can assume that the dataacquired by each coil can be given by, for example:

m _(l) =F·S _(l) ·d,  [1]

where d can be the image series to be reconstructed in the Cartesianx-y-t space, m_(l) can be the acquired radial data for the l-th coilelement, F can be the non-uniform FFT NUFFT operator defined on theradial acquisition pattern, and S_(l) can be the sensitivity map for thel-th coil in the Cartesian x-y space.

To facilitate joint multicoil sparsity, the exemplary GRASP procedurecan concatenate the individual coil models to form the followingmulticoil model, which can be, for example:

m=E·d,  [2]

where

${m = \begin{bmatrix}m_{1} \\\vdots \\m_{c}\end{bmatrix}},{E = {F \cdot \begin{bmatrix}S_{1} \\\vdots \\S_{c}\end{bmatrix}}}$

and c can be the number of coils. The GRASP reconstruction can then begiven by, for example:

x=argmin{∥E·d−m∥ ₂ ² +λ∥T·d∥ ₁},  [3]

where T can be the sparsifying transform, ∥ ∥₁ can be the l₁ normdefined as ∥x∥₁=Σ_(i)|x_(i)|, and ∥x∥₂ can be the l₂ norm defined as∥x∥₂=(Σ_(i)|x_(i)|²)^(1/2). The l₁-norm term can facilitate a jointsparsity in the sparse domain given by T and the l₂-norm term canenforce parallel imaging data consistency. λ can be a regularizationparameter that can control the tradeoff between data consistency andsparsity. Eq. [3] can be implemented using an iterative non-linearconjugate gradient procedure. Instead of finding the optimal value of λfor each data set, the value of λ can be decreased during theiterations, such that high-value coefficients can be recovered first andlow-value coefficients can be recovered in later iterations. Thereconstruction procedure can allow the utilization of one sparsifyingtransform or a combination of sparsifying transforms by adding extral₁-norm terms.

The exemplary reconstruction procedure can incorporate a target shapefor each exemplary reconstructed temporal frame. The exemplaryreconstruction can assume a boxcar shape with an extent given by theduration of the consecutive spokes used for each temporal frame. Thisexemplary approach can give equal weight to all spokes within a temporalframe, which might not optimal. If exemplary embodiments choose a targetshape for each temporal frame, such as a sine, Hamming, or Kaiserfunction, the data consistency part of the reconstruction can berepresented as a fit of the acquired k-space data to this targettemporal shape.

Following data sorting, exemplary SG-GRASP reconstruction can beperformed following the GRASP procedure described in (See, e.g.,Reference 16). For SG-MP-GRASP, where data can have increaseddimensionality, the reconstruction can be extended to minimize thefollowing objective function ∥E·x−y∥₂+λ₁∥T₁·x∥₁+λ₂∥T₂·x∥₁+ . . .+λ_(n)∥T_(n)·x∥₁, where x can be the image to be reconstructed, y can bethe sampled measurements in radial k-space and E can be the Fouriertransform operator incorporating NUFFT operation (See e.g., Reference18). T_(n) can be the sparsifying transform performed along the n^(th)dynamic dimension and λ_(n) can be the weighting parameter. For staticimaging, n=1 which can be the additionally constructed respiratorydimension and for dynamic imaging, n>=2 including the original dynamicdimensions (e.g., cardiac contraction) and the respiratory dimension. Inthe reconstruction, only temporal sparsifying transforms can be used andthe λ's can be empirically determined by comparing the performance ofseveral values.

Exemplary Further Image Construction

In a conventional “stack of stars” approach to 3D sampling of k-space,with or without golden-angle ordering of the radially sampledacquisitions, the “IQ” direction, orthogonal to the radially sampleddirections, may only be sampled at a discrete set of uniformly spacedlocations in the k2 dimension. This highly ordered sampling arrangementmay not be optimal for the use in CS reconstruction methods, whichperform best with uncorrelated locations of the sampled data. However,this can be improved by using different novel approaches to the samplingof the k_(z) dimension, as described below.

One exemplary procedure to improve on a stack-of-stars samplingprocedure can be to replace the current approach, which can use sets ofradial samples regularly spaced along the k_(z) dimension, which can behighly ordered and leaves large regions of k, dimension data unsampledbetween the sampled planes, with a pseudorandom positioning along the kdimension of the radially oriented sets of k-space samples (e.g.,relative to the k_(z)-k_(z) plane). The sets of radial samples can thenbe distributed within a cylindrical “rod” 605 in k-space, rather thanjust lying on a set of regularly spaced planes, and can fill in some ofthe otherwise unsampled locations (See e.g., FIG. 6). This kind of“rod-of-rays” sampling geometry can lend itself readily to CS imagereconstruction methods, which can benefit from the higher degree of lackof correlation, or “incoherence”, of the sampled locations that itprovides, resulting in improved image quality. Such incoherence can bestandard in compressed sensing image reconstruction methods. This methodalso facilitates the use of a non-uniform density of the distribution ofthe sample locations in k-space, such as is described below, which canalso provide further improvements in image quality, particularly forincreasing the effective field of view along the z direction at the costof additional computation in the image reconstruction process. Thisimprovement in imaging performance can also be used to decrease thenumber of samples to be acquired for image reconstruction, and canincrease imaging speed or improve temporal resolution in dynamicimaging.

In exemplary dynamic imaging applications for use with time-varyingobjects, such as sequential imaging of moving objects or the dynamics ofcontrast enhancement, the order of the acquisition of the k-spacesamples can be significant. For planar radial sampling, golden-angleordering of the sampling directions can provide several advantages overprevious approaches (e.g., simple linear sequential ordering of thesampling), such as maintaining a quasi-uniform sampling densitythroughout the sampling process. The exemplary segment of the k_(z)dimension that can be sampled can be treated as being mapped along thecircumference of an equivalent circle 700, and a golden-angle procedurecan be used to choose sequential sample locations along this remappeddimension (See, e.g., FIG. 7). The same benefits of quasi-uniformdensity of sampling along the IQ dimension can be achieved throughout acontinuous sampling process, as can be achieved with the conventionalgolden-angle angular sampling, with the attendant improved flexibilityfor making adaptive choices of the temporal resolution, and samplingdensity of the reconstructed images during the image reconstructionprocess, through flexible choices of the subsegments of the acquireddata to be reconstructed. Thus, in a Golden-angle Radial Ordering of thesampling Distribution (“GoldenROD”) for the full 3D k-space sampling tobe used in the image reconstruction can be generated.

In both the conventional stack-of-stars approach to IQ dimensionsampling and the exemplary simple golden-angle k_(z) sampling proceduredescribed above, there can be an approximately uniform distribution ofthe samples along the k_(z) dimension. However, the exemplarygolden-angle sampling scheme can be further modified so as to facilitatethe use of an arbitrary desired distribution of the sampled locationsalong the k_(z) dimension (See e.g., FIGS. 8A-8C). This can be achievedthrough first performing a nonlinear remapping of the actual k_(z)dimension to an equivalent “warped” k_(z)′ dimension, and thenperforming the same sort of wrapping of the segment of the k_(z)′dimension to be sampled around the circumference of a circle 800 (Seee.g., FIG. 8A). Using a golden-angle sampling procedure to choosesequential sampling locations within the remapped k_(z)′ as describedabove, can achieve a quasi-uniform sampling distribution in the k_(z′)dimension (See e.g., FIG. 8B), however, there can be a reciprocal (e.g.,non-uniform) sampling density in the original k_(z) dimension when thesample locations are re-mapped back to the original k_(z) space (Seee.g., FIG. 8C). For example, if the middle of the region of 815 FIG. 8Cis expanded in a dimension to be sampled and contract ends, inperforming the remapping prior to applying the golden-angle sampling,the resulting sampling of the original k dimension can have an increaseddensity of samples in the middle of k-space, which can be where most ofthe image energy resides, and a decreased density of sample at theedges. This can provide a generally more efficient way to samplek-space, and can result in improved image quality.

A further exemplary approach can be used for 3D MR imaging, as analternative to the stack-of-stars approach to k-space sampling describedabove, can be the “stack-of-spirals”, where the set of radial rays ofsamples in the k_(x)-k_(y) plane used in the stack-of-stars approachshown in FIG. 1E can be replaced by a set of single or interleavedspiral paths 150 in the k_(x)-k_(y) plane. In conventional approaches tothe use of stack-of-spirals imaging, these spiral sets of samples can bechosen to be located on a discrete set of planes along the k_(z)direction, with the same resulting relative disadvantage for CS imagereconstructions as with the conventional stack-of stars imaging samplingprocedure. However, the exemplary golden-angle methods described abovecan be adapted for selecting k locations for stack-of-stars sampling,and use them as a means for similarly selecting k locations for thespiral sample paths used in stack-of-spirals imaging. In this manner,spiral sets of samples can be acquired with any desired, andnon-discrete and non-repeating, distribution of locations along the k,direction, creating an effectively more continuously sampled rod-likevolume of k-space or “stick-of-spirals”. Thus, data can be continuouslyacquired can be better suited to CS reconstruction methods than theconventional stack-of-spirals imaging method, with the same associatedability to more flexibly choose different subsegments of the data forimage reconstruction described above for the rod-of-rays approach tosampling.

A further exemplary approach that can be used for data acquisition for3D MRI can be the use of radial rays oriented toward the surface of asphere in k-space, rather than toward the surface of a cylinder, as canbe used with the stack-of-stars approach. (See e.g., FIG. 8D). Theexemplary golden-angle sampling approach that can be used for 2D anglelocations of the sampled directions in the stack-of-stars method can beadapted to this kind of 3D radial sampling. An approximately uniformdistribution of the sampling locations over the surface of the sphere ink-space can be used in the image reconstruction. If the equator of thesphere can be designated as lying in the k_(x)-k_(y) plane, with the k,axis running through the equators, the angular locations of the sampledrays relative to the equator can be chosen, for example, parameterizedby the “azimuthal” angle 0, as with the conventional golden-angleapproach to 2D radial imaging, with an approximately uniformdistribution of non-repeating sample locations relative to ⊖ (825).However, the locations of the sampled rays on the sphere relative to theremaining (“altitude”) angle φ (830) may not be simply chosen in thesame way relative to φ (830) with golden angle increments producing anapproximately uniform distribution over φ (830). This can be because thecorresponding fractional area of the sphere associated with p can go inconjunction with the cosine of the angle. This can result in acorrespondingly non-uniform reciprocal distribution of the density ofsampling locations per unit area over the sphere, with sampling pointsnear the polar regions being disproportionately represented relative tothose near the equator, for example, with density of sampled locationson the sphere distributed approximately as 1/(cos φ). However, anonlinear remapping of the locations along p to corresponding locationsalong the corresponding normalized k_(z) axis, k_(z)=sin(φ) can be used.An exemplary golden-angle sampling procedure which can produce anapproximately uniform distribution of sampling locations along k_(z), asdescribed above, can produce a corresponding non-uniform distribution ofthe locations along the original φ (830), such that the net distributionof the final sampling locations, with choices of sample locations along⊖ (825) and k_(z) determined by golden-angle ordering of the locationswithin each angular parameter range, can be approximately uniformlydistributed over the sphere parameterized by ⊖ (825) and φ (830). Thiscan facilitate the same kind of continuous acquisition of approximatelyuniformly distributed, but non-repeating, k-space data from dynamicobjects as described above for the exemplary golden-angle cylindricalsampling procedures, with the same associated ability to flexibly choosesubsegments of the data for serial image reconstructions. Such anapproach to 3D radial golden-angle sampling has been previously proposed(See, e.g., Reference 20); however, this approach was not applied to theselection of the sampling locations along k_(z).

An exemplary implementation of the stack-of-stars sampling procedure,and the variants described above, can be to acquire frequency-encodedradial samples of k-space relative to the k_(x)-k_(y) plane, with signaldetections in the presence of a set of radially oriented magnetic fieldgradients (“gradients”) in the x-y plane, after the application ofsuitably incremented sets of values of a pulse of gradient along the zdirection for phase encoding along the k direction. However, analternative exemplary approach can also be used for acquisition of datawith the same kind of stack-of-stars sampling procedure, with the use ofsignal detections in the presence of a frequency-encoding gradientoriented longitudinally along the z direction, after the application ofsuitably incremented sets of values of a pulse of gradient in the x-yplane for phase encoding in order to move the resulting line of samplesalong the k direction to different locations in the k_(x)-k_(y) plane.This can be chosen with golden-angle sampling methods, as describedabove.

The conventional exemplary approach to implementing this version ofstack-of-stars sampling, with the sampled points in lying on a discreteset of planes, can suffer from the same relative lack of incoherence ofthe sampling along the k_(z) direction as other conventionalstack-of-stars sampling method, thus potentially reducing its usefulnessfor compressed sampling types of reconstruction. However, the exemplarysampling procedure can be generalized, and can overcome this potentiallimitation by also adding a suitably incremented set of gradient pulsesalong the z direction before the signal detections, in order to offsetthe locations of the samples along the k_(z) direction. In particular,the same exemplary golden-angle sampling approach as above can be usedto find a series of such offsets, ranging in size between zero and thespacing of the samples along the k direction. The resulting data set canmore uniformly sample the rod-like volume of the cylindrical region ofk-space, in a non-repeating way, with an expected resulting improvementin the quality of the associated compressed sensing imagereconstructions. However, this “jittering” of the k, sample locationscan be unlikely, as the samples can be collected very densely along thefrequency-encoded direction by sampling the signal rapidly in timeduring the signal detection process.

Exemplary Application to Contrast-Enhanced Abdominal MRI

An assessment of post-contrast multi-phase acquisitions (e.g., inarterial and venous phases of enhancement) can be essential for liverlesion detection and characterization. Dynamic post-contrast liver MRexamination can be performed using a Tl-weighted fat-saturated 3Dvolumetric interpolated (“VIBE”) pulse sequence with Cartesian k-spacesampling in a breath-hold (“BH”). However, this acquisition can besensitive to respiratory motion and can result in suboptimal images inpatients who cannot adequately breath-hold, such as elderly,debilitated, or pediatric patients. Although parallel-imaging andpartial-Fourier techniques can be employed to accelerate dataacquisition, and reduce sensitivity to respiratory motion, in-planespatial resolution and anatomic coverage that can be achieved can remainlimited due to the need to acquire data within a breath-hold.

According to certain exemplary embodiments of the present disclosure, ahighly-accelerated free-breathing 3D contrast-enhanced liver MRItechnique can be provided with high spatial and temporal resolution, forexample using GRASP with temporal TV as a sparsifying transform. FIG. 9shows exemplary graphs and images of exemplary results of afree-breathing exam with a 3D stack-of-stars (e.g., radial sampling fork_(y)-k_(x) and Cartesian sampling for k_(z)) FLASH pulse sequence withgolden-angle procedure. Exemplary imaging parameters can include:FOV=380×380 mm², base resolution=384 for each radial spoke, slicethickness=3 mm, and TE/TR=1.7/3.9 ms. Six hundred spokes can becontinuously acquired for each of 30 slices during free-breathing, tocover the entire liver with a total acquisition time of 77 seconds(e.g., 2 seconds 960, 15 seconds 965, and 60 seconds 970). The same dataset can be employed to reconstruct dynamic MRI with three differenttemporal resolutions of 2.5 seconds (e.g., 21 spokes/frame 510), 1.5seconds (e.g., 13 spokes/frame 920) and 0.9 seconds (e.g. 8spokes/frames 930). Exemplary reconstructions can present adequatespatial and temporal behavior with a small increase in residual aliasingartifacts for higher accelerations, as can be expected from the highundersampling factor employed. These high temporal resolutions canrepresent a significant gain over traditional techniques employed inclinical studies, and can be useful for liver perfusion studies withhigh spatial resolution and whole-abdomen coverage. The exemplaryreconstructed image matrix size can be 384×384 for each of the 30 slicescovering the whole abdomen with in-plane spatial resolution of 1 mm andslice thickness of 3 mm. Column 940 in FIG. 9 shows the exemplary imagescorresponding to three different temporal frames, and column 950illustrates the signal-intensity time courses for the aorta and portalvein.

Exemplary Application to Cardiac Cine MRI

Cardiac cine MRI procedures can be a valuable technique for assessmentof myocardial function. Cine techniques can be used to deal with thechallenge of respiratory motion, particularly in patients who cannothold their breath. According to exemplary embodiments of the presentdisclosure, a free-breathing 2D cine within a single heartbeat andwhole-heart 3D cine within a single breath-hold can be provided whichcan use the exemplary GRASP technique with temporal TV as sparsifyingtransform. For example, a Steady State Free Precession (“SSFP”) pulsesequence with radial sampling using the golden-angle scheme can beemployed for data acquisition. For 2D cine, 500 continuous spokes can beacquired during 1.5 seconds and groups of 8 consecutive spokes can beused to form a temporal frame, resulting in a temporal resolution of20.8 ms (e.g., 50 fps). Exemplary parameters for 2D cine can includeFOV=400×400 mm², slice-thickness=10 mm, image matrix=192×192, spatialresolution=2×2 mm², and TE/TR=2.6/1.3 ms.

Exemplary cardiac cine imaging can be performed on a healthy volunteer(e.g., male, age=26). In one example, this can be done during freebreathing without external cardiac or respiratory gating in a 3T MRIscanner (e.g., TimTrio, Siemens) with a 12-element receive coil. A 2Dsteady-state free processing (“SSFP”) pulse sequence with GA radialsampling can be employed to acquire one mid short axis slice with matrixsize=192×192. 4800 continuous spokes can be acquired in 15 s including a1 s dummy scan for steady state. FOV=320×320 mm, slice thickness=10 mm,TR/TE=3.1/1.34 ms and FA=50_(o). SG-GRASP reconstruction can beperformed using data acquired during expiration with matrixsize=192×192×30, where 30 phases can be reconstructed for one cardiaccycle. The entire data set can also be sorted into 6 respiratory phasesfor SG-MP-GRASP reconstruction with matrix size=192×192×30×6. 24 spokescan be used for each phase, which can correspond to an acceleration rateof 12.6. Liver imaging can be performed on a further volunteer (e.g.,male, age=29) during free breathing without external gating in the sameMRI scanner. A 3D TurboFLASH pulse sequence with stack of stars GAradial sampling can be implemented, and 14 slices can be acquired incoronal view with in-plane matrix size=224×224. 1000 continuous spokescan be acquired for each slice with FOV=300×300 mm, slice thickness=10mm, TR/TE=3.47/1.52 ms and FA=12_(o). SG-GRASP (e.g., static images)reconstruction can be performed using data acquired during expirationwith matrix size=224×224×14 and SG-MP-GRASP (e.g., dynamic images)reconstruction can be performed by sorting the whole data set into 6respiratory phases with matrix size=224×224×14×25. 40 spokes can be usedfor each phase, which can correspond to an acceleration rate of 8.8.

Exemplary reconstruction can be implemented in MATLAB (e.g., MathWorks,MA) using a non-linear conjugate gradient procedure and total variation(“TV”) as the sparsifying transform for each temporal dimension. ForSG-GRASP reconstruction in liver data, 2D spatial TV can be used as thesparsifying transform due to the lack of temporal dimension. Theweighting parameters can be chosen empirically after comparing theperformance of different values.

For 3D cine, a stack-of-stars trajectory (e.g., radial along k_(y)-k_(x)and Cartesian along k_(z)) can be employed. For each partition, forexample about 320 spokes can be acquired during each heartbeat for atotal of 30 heartbeats and 8 consecutive spokes can be employed to forma temporal frame (e.g., acquisition window=22.4 ms). Exemplaryparameters for 3D cine can include image matrix=192×192×40, spatialresolution=2×2×3 mm², and TE/TR=2.8/1.4 ms. FIG. 10 illustratesexemplary images of exemplary reconstruction results with good imagequality for free-breathing 2D cardiac cine in only 1.5 seconds (e.g.,images 1010 and 1015) and whole-heart 3D cine (e.g., images 1020 and1025) within a single breath-hold using GRASP. The exemplary image 1010is of a free-breathing 2D cardiac cine within a single heartbeat with atemporal resolution of 50 fps for short axis views, while the exemplaryimage 1015 is for long axis views, both using GRASP with only 8spokes/frames. The exemplary images 1020 and 1025 illustrate a 3Dcardiac cine within a single breath-hold for three different slices atend-diastole 1025 and end-systole 1020 cardiac phases using GRASP with 8spokes/frame.

FIG. 11A shows representative exemplary cardiac cine images ofend-diastole and end-systole from SG-GRASP (e.g., 1 respiratory phase)and FIG. 11B shows exemplary representative cardiac cine images ofend-diastole and end-systole from SG-MP-GRASP (e.g., 6 respiratoryphases). Both reconstruction images provided in FIGS. 11A and 11B canpresent adequate image quality with SG-MP-GRASP having improvedperformance as demonstrated by the lower level of residual aliasingartifact when cine movies can be played (not shown). FIG. 12A shows anexemplary liver image from a representative partition withoutself-gating. FIG. 12B shows an exemplary liver image from SG-GRASP(e.g., 1 respiratory phase) and FIG. 12C shows image from SG-MP-GRASP(e.g., 25 respiratory phases). Sharper liver vessels can be seen in FIG.12C.

Exemplary Properties of Exemplary Embodiments

In certain exemplary embodiments of the present disclosure, it can bepossible to significantly reduce many of the major limitations ofcurrent MRI techniques, such as imaging speed and complexity, and theirconsequences. Using an exemplary method and system according to thepresent disclosure, it can be possible to utilize a combination ofcompressed sensing, parallel imaging and golden-angle radial sampling toachieve high performance MRI studies with improved combinations oftemporal resolution, spatial resolution and volumetric coverage.Furthermore, according to further exemplary embodiments of the presentdisclosure, it can be possible to provide and/or utilize data that canbe continuously acquired without interruption during free-breathing fora certain period of time and image reconstruction can be performed withuser-defined temporal frames (e.g., position, resolution and shape).

Continuous data acquisition can represent a preferred and/or optimal useof an MRI scanner, unlike in current free-breathing MRI techniques usingnavigators, where most of the data is discarded if they can be outside aregion of moderate motion. The flexibility of the exemplaryreconstruction approach can facilitate a high impact for clinicalstudies, particularly for contrast-enhanced examinations, since theadditional data acquisition can be used to get information with highertemporal resolution. In exemplary embodiments, it can be possible usecontinuous acquisition of radial data with and for the exemplarygolden-angle scheme and reconstruction with arbitrary temporalresolution, along with compressed sensing and parallel imaging to offera significant improvement, for example in the reconstruction of highlyundersampled data.

According to the exemplary embodiments of the present disclosure, it cantherefore be possible to provide an improvement in performance comparedto traditional techniques used in clinical studies, which can rely onbreath-held or navigated free-breathing examinations. Moreover, it canbe possible to simplify the way MRI procedures can be performed, forexample by using a continuous data acquisition approach, without havingto carefully select the temporal frames to acquire.

Exemplary GRASP MRI Arrangement System

FIG. 13 shows a block diagram of an exemplary embodiment of a systemaccording to the present disclosure. For example, exemplary proceduresin accordance with the present disclosure described herein can beperformed by a processing arrangement and/or a computing arrangement1310 and a GRASP MRI arrangement 1380. GRASP MRI arrangement 1380 caninclude computer executable instructions and/or MRI technology. Suchprocessing/computing arrangement 1310 can be, for example entirely or apart of, or include, but not limited to, a computer/processor 1320 thatcan include, for example one or more microprocessors, and useinstructions stored on a computer-accessible medium (e.g., RAM, ROM,hard drive, or other storage device).

As shown in FIG. 13, for example a computer-accessible medium 1330(e.g., as described herein above, a storage device such as a hard disk,floppy disk, memory stick, CD-ROM, RAM, ROM, etc., or a collectionthereof) can be provided (e.g., in communication with the processingarrangement 1310). The computer-accessible medium 1330 can containexecutable instructions 1340 thereon. In addition or alternatively, astorage arrangement 1350 can be provided separately from thecomputer-accessible medium 1330, which can provide the instructions tothe processing arrangement 1310 so as to configure the processingarrangement to execute certain exemplary procedures, processes andmethods, as described herein above, for example.

Further, the exemplary processing arrangement 1310 can be provided withor include an input/output arrangement 1370, which can include, forexample a wired network, a wireless network, the internet, an intranet,a data collection probe, a sensor, etc. As shown in FIG. 13, theexemplary processing arrangement 1310 can be in communication with anexemplary display arrangement 1360, which, according to certainexemplary embodiments of the present disclosure, can be a touch-screenconfigured for inputting information to the processing arrangement inaddition to outputting information from the processing arrangement, forexample. Further, the exemplary display 1360 and/or a storagearrangement 1350 can be used to display and/or store data in auser-accessible format and/or user-readable format.

The foregoing merely illustrates the principles of the disclosure.Various modifications and alterations to the described embodiments canbe apparent to those skilled in the art in view of the teachings herein,and especially in the appended numbered paragraphs. It can thus beappreciated that those skilled in the art can devise numerous systems,arrangements, and methods which, although not explicitly shown ordescribed herein, embody the principles of the disclosure and are thuswithin the spirit and scope of the disclosure. In addition, allpublications and references referred to above are incorporated herein byreference in their entireties. It should be understood that theexemplary procedures described herein can be stored on any computeraccessible medium, including a hard drive, RAM, ROM, removable disks,CD-ROM, memory sticks, etc., and executed by a processing arrangementwhich can be a microprocessor, mini, macro, mainframe, etc. In addition,to the extent that the prior art knowledge has not been explicitlyincorporated by reference herein above, it is explicitly beingincorporated herein in its entirety. All publications referenced aboveare incorporated herein by reference in their entireties.

EXEMPLARY REFERENCES

The following references are hereby incorporated by reference in theirentirety.

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1. A non-transitory computer-accessible medium having stored thereoncomputer-executable instructions for reconstructing data associated withat least one object, wherein, when a computer hardware arrangementexecutes the instructions, the computer arrangement is configured toperform procedures comprising: acquiring radial data based on agolden-angle procedure; sorting the acquired radial data into at leastone time-series having an arbitrary temporal resolution; andreconstructing the data using a compressed sensing procedure and aparallel imaging procedure based on the sorted data.
 2. Thecomputer-accessible medium of claim 1, wherein the radial data includesmagnetic resonance imaging data.
 3. The computer-accessible medium ofclaim 1, wherein the radial data comprises a plurality of radial lines.4-6. (canceled)
 7. The computer-accessible medium of claim 3, whereinthe reconstruction procedure is performed based on a first group ofconsecutive ones of the radial lines used to generate at least onetemporal frame.
 8. The computer-accessible medium of claim 7, whereinthe reconstruction procedure is performed based on a second group of theconsecutive ones of the radial lines used to generate at least onefurther temporal frame, the second group having different radial linesthan the first group.
 9. The computer-accessible medium of claim 7,wherein the reconstruction procedure is performed based on a targetshape for each temporal frame.
 10. (canceled)
 11. Thecomputer-accessible medium of claim 3, wherein the reconstructionprocedure is performed at arbitrary time points by centering a group ofconsecutive ones of the radial lines at different points during anacquisition period.
 12. The computer-accessible medium of claim 1,wherein the acquiring procedure comprises acquiring all slices for agiven projection for a particular golden-angle before proceeding to anext golden-angle.
 13. (canceled)
 14. The computer-accessible medium ofclaim 13, wherein the reconstruction procedure is performed based on aphysiological motion of at least one anatomical structure.
 15. Thecomputer-accessible medium of claim 14, wherein the physiological motionis an expiratory phase of the at least one anatomical structure.
 16. Thecomputer-accessible medium of claim 15, wherein the expiratory phase isbased on a respiratory motion signal of the at least one anatomicalstructure.
 17. (canceled)
 18. The computer-accessible medium of claim 1,wherein the reconstruction procedure is performed based on coilsensitivity maps of at least one exemplary multicoil reference image.19. (canceled)
 20. The computer-accessible medium of claim 1, whereinthe reconstruction procedure is performed based on sorting the radialdata into highly undersampled temporal frames by grouping a particularnumber of consecutive ones of the radial lines to form each temporalframe.
 21. The computer-accessible medium of claim 20, wherein theparticular number is a Fibonacci number.
 22. The computer-accessiblemedium of claim 1, wherein the radial data is based on k-space samplingof the at least one object.
 23. The computer-accessible medium of claim22, wherein the k-space sampling is performed using a stack-of-starsprocedure.
 24. The computer-accessible medium of claim 22, wherein thek-space sampling is performed using a stack-of-spiral procedure.
 25. Thecomputer-accessible medium of claim 1, wherein the step of acquiringradial data is performed continuously during the reconstructionprocedure.
 26. A method for reconstructing data associated with at leastone object, comprising: acquiring radial data based on a golden-angleprocedure; sorting the acquired radial data into at least onetime-series having an arbitrary temporal resolution; and using acomputer arrangement, reconstructing the data using a compressed sensingprocedure and a parallel imaging procedure based on the sorted data.27-50. (canceled)
 51. A system for reconstructing data associated withat least one object, comprising: a computing arrangement which isconfigured to: a. acquiring radial data based on a golden-angleprocedure; b. sorting the acquired radial data into at least onetime-series having an arbitrary temporal resolution; and c.reconstructing the data using a compressed sensing procedure and aparallel imaging procedure based on the sorted data. 52-75. (canceled)